Pooled Variance
pooled variance (also known as combined, composite, or overall variance) is a method for estimating variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same. The numerical estimate resulting from the use of this method is also called the pooled variance.
Under the assumption of equal population variances, the pooled sample variance provides a higher precision estimate of variance than the individual sample variances. This higher precision can lead to increased statistical power when used in statistical tests that compare the populations.
The pooled variance is an estimate of the fixed common variance \[\sigma ^{2} \] underlying various populations that have different means.
Formula used
The unbiased least squares estimate of \[\sigma ^{2} \]
\[s_{p}^{2} =\frac{\sum _{i=1}^{k}\left ( n_{i} -1\right )s_{i}}{\sum _{i=1}^{k}\left ( n_{i} -1\right )} \]
and the biased maximum likelihood estimate
\[s_{p}^{2} =\frac{\sum _{i=1}^{k}\left ( n_{i} -1\right )s_{i}}{\sum _{i=1}^{k} n_{i} } \]
